Internal structure of polymer chains

The asymptotic behaviour of isolated long chain polymers in good solvents is modelled well by the self-avoiding walk on a regular crystal lattice. In this paper we investigate the typical scaling length and the probability distribution function for the position of the end point and an interior point for self-avoiding walks on a simple cubic lattice. We find that for N-step walks the typical internal scaling length, RN(n), associated with the position of the nth step, has a similar functional form to the external scaling length, RN. The associated exponent ν is found to be the same for both scaling lengths, within the confidence limits of our simulations. The internal probability distribution function, pN(n,r), is shown to be skew-Gaussian and furthermore has a similar form to the external distribution function: pN(n,r) ≈ [r/RN(n)]aexp{−[r/RN(n)δ}, where a = 2.42 ± 0.08 and δ = 2.50 ± 0.09